Yes. Absolutely. The Toshiba R850 has 2 SODIMM slots. If the configuration you purchased, with 4GB of ram, has a single 4GB SODIMM, then all you need do is buy a second 4GB module. If it comes with 2x2GB then you need to replace both. However, DDR3 memory is so cheap right now, it hardly matters as you can pick up an 8GB kit (2x4GB) for less than $40 (USD).

All you need to do is remove a single screw on the center panel on the underside to access the SODIMM (ram) slots. Here is a youtube video showing you how to do it with this very laptop.